Determine whether the statement is true or false. If f '(c) = 0, then f has a local maximum or minimum at c. TrueFalse Determine whether the statement is true or false. If f has an absolute maximum value at c, then f '(c) = 0. TrueFalse Determine whether the statement is true or false. If f is differentiable and f(−7) = f(7), then there is a number c such that |c| < 7 and f '(c) = 0. TrueFalse Determine whether the statement is true or false. If f '(x) = g'(x) for 0 < x < 1, then f(x) = g(x) for 0 < x < 1. TrueFalse Determine whether the statement is true or false. If f and g are increasing on an interval I, then fg is increasing on I. TrueFalse Determine whether the statement is true or false. If f is decreasing and f(x) > 0 on I, then g(x) = 1/f(x) is increasing on I. TrueFalse Determine whether the statement is true or false. If f is periodic and f is differentiable, then f ' is periodic. TrueFalse Determine whether the statement is true or false. If f '(x) < 0 for 1 < x < 4, then f is decreasing on (1, 4). TrueFalse Determine whether the statement is true or false. There exists a function f such that f(x) > 0, f '(x) < 0, and f ''(x) > 0 for all x. TrueFalse Determine whether the statement is true or false. If f '(x) exists and is nonzero for all x, then f(1) ≠ f(0). TrueFalse
Determine whether the statement is true or false. If f '(c) = 0, then f has a local maximum or minimum at c. TrueFalse Determine whether the statement is true or false. If f has an absolute maximum value at c, then f '(c) = 0. TrueFalse Determine whether the statement is true or false. If f is differentiable and f(−7) = f(7), then there is a number c such that |c| < 7 and f '(c) = 0. TrueFalse Determine whether the statement is true or false. If f '(x) = g'(x) for 0 < x < 1, then f(x) = g(x) for 0 < x < 1. TrueFalse Determine whether the statement is true or false. If f and g are increasing on an interval I, then fg is increasing on I. TrueFalse Determine whether the statement is true or false. If f is decreasing and f(x) > 0 on I, then g(x) = 1/f(x) is increasing on I. TrueFalse Determine whether the statement is true or false. If f is periodic and f is differentiable, then f ' is periodic. TrueFalse Determine whether the statement is true or false. If f '(x) < 0 for 1 < x < 4, then f is decreasing on (1, 4). TrueFalse Determine whether the statement is true or false. There exists a function f such that f(x) > 0, f '(x) < 0, and f ''(x) > 0 for all x. TrueFalse Determine whether the statement is true or false. If f '(x) exists and is nonzero for all x, then f(1) ≠ f(0). TrueFalse
Determine whether the statement is true or false. If f '(c) = 0, then f has a local maximum or minimum at c. TrueFalse Determine whether the statement is true or false. If f has an absolute maximum value at c, then f '(c) = 0. TrueFalse Determine whether the statement is true or false. If f is differentiable and f(−7) = f(7), then there is a number c such that |c| < 7 and f '(c) = 0. TrueFalse Determine whether the statement is true or false. If f '(x) = g'(x) for 0 < x < 1, then f(x) = g(x) for 0 < x < 1. TrueFalse Determine whether the statement is true or false. If f and g are increasing on an interval I, then fg is increasing on I. TrueFalse Determine whether the statement is true or false. If f is decreasing and f(x) > 0 on I, then g(x) = 1/f(x) is increasing on I. TrueFalse Determine whether the statement is true or false. If f is periodic and f is differentiable, then f ' is periodic. TrueFalse Determine whether the statement is true or false. If f '(x) < 0 for 1 < x < 4, then f is decreasing on (1, 4). TrueFalse Determine whether the statement is true or false. There exists a function f such that f(x) > 0, f '(x) < 0, and f ''(x) > 0 for all x. TrueFalse Determine whether the statement is true or false. If f '(x) exists and is nonzero for all x, then f(1) ≠ f(0). TrueFalse
If f '(c) = 0, then f has a local maximum or minimum at c.
TrueFalse
Determine whether the statement is true or false.
If f has an absolute maximum value at c, then f '(c) = 0.
TrueFalse
Determine whether the statement is true or false.
If f is differentiable and
f(−7) = f(7),
then there is a number c such that
|c| < 7
and
f '(c) = 0.
TrueFalse
Determine whether the statement is true or false.
If
f '(x) = g'(x)
for
0 < x < 1,
then
f(x) = g(x)
for
0 < x < 1.
TrueFalse
Determine whether the statement is true or false.
If f and g are increasing on an interval I, then fg is increasing on I.
TrueFalse
Determine whether the statement is true or false.
If f is decreasing and
f(x) > 0
on I, then
g(x) = 1/f(x)
is increasing on I.
TrueFalse
Determine whether the statement is true or false.
If f is periodic and f is differentiable, then f ' is periodic.
TrueFalse
Determine whether the statement is true or false.
If
f '(x) < 0
for
1 < x < 4,
then f is decreasing on
(1, 4).
TrueFalse
Determine whether the statement is true or false.
There exists a function f such that
f(x) > 0,
f '(x) < 0,
and
f ''(x) > 0
for all x.
TrueFalse
Determine whether the statement is true or false.
If f '(x) exists and is nonzero for all x, then
f(1) ≠ f(0).
TrueFalse
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
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